THE WEIERSTRASS SUBGROUP OF A CURVE HAS MAXIMAL RANK

The Weierstrass Subgroup of a Curve Has Maximal Rank

We show that the Weierstrass points of the generic curve of genus g over an algebraically closed field of characteristic 0 generate a group of maximal rank in the Jacobian. The Weierstrass points are a set of distinguished points on curves, which are geometrically intrinsic. In particular, the group these points generate in the Jacobian is a geometric invariant of the curve. A natural question ...

On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Weierstrass Pure Gaps From a Quotient of the Hermitian Curve

In this paper, by employing the results over Kummer extensions, we give an arithmetic characterization of pure gaps at many totally ramified places over the quotients of Hermitian curves, including the well-studied Hermitian curves as special cases. The cardinality of these pure gaps is explicitly investigated. In particular, the numbers of gaps and pure gaps at a pair of distinct places are de...

The Maximal Rank Conjecture

Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this paper, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C ⊂ Pr.